The role of initial geometry in experimental models of wound closing

Wound healing assays are commonly used to study how populations of cells, initialised on a two-dimensional surface, act to close an artificial wound space. While real wounds have different shapes, standard wound healing assays often deal with just one simple wound shape, and it is unclear whether varying the wound shape might impact how we interpret results from these experiments. In this work, we describe a new kind of wound healing assay, called a sticker assay, that allows us to examine the role of wound shape in a series of wound healing assays performed with fibroblast cells. In particular, we show how to use the sticker assay to examine wound healing with square, circular and triangular shaped wounds. We take a standard approach and report measurements of the size of the wound as a function of time. This shows that the rate of wound closure depends on the initial wound shape. This result is interesting because the only aspect of the assay that we change is the initial wound shape, and the reason for the different rate of wound closure is unclear. To provide more insight into the experimental observations we describe our results quantitatively by calibrating a mathematical model, describing the relevant transport phenomena, to match our experimental data. Overall, our results suggest that the rates of cell motility and cell proliferation from different initial wound shapes are approximately the same, implying that the differences we observe in the wound closure rate are consistent with a fairly typical mathematical model of wound healing. Our results imply that parameter estimates obtained from an experiment performed with one particular wound shape could be used to describe an experiment performed with a different shape. This fundamental result is important because this assumption is often invoked, but never tested

The topography of multivariate normal mixtures

Multivariate normal mixtures provide a flexible method of fitting high-dimensional data. It is shown that their topography, in the sense of their key features as a density, can be analyzed rigorously in lower dimensions by use of a ridgeline manifold that contains all critical points, as well as the ridges of the density. A plot of the elevations on the ridgeline shows the key features of the mixed density. In addition, by use of the ridgeline, we uncover a function that determines the number of modes of the mixed density when there are two components being mixed. A followup analysis then gives a curvature function that can be used to prove a set of modality theorems.Comment: Published at http://dx.doi.org/10.1214/009053605000000417 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A simple mechanistic model of sprout spacing in tumour-associated angiogenesis

This paper develops a simple mathematical model of the siting of capillary sprouts on an existing blood vessel during the initiation of tumour-induced angiogenesis. The model represents an inceptive attempt to address the question of how unchecked sprouting of the parent vessel is avoided at the initiation of angiogenesis, based on the idea that feedback regulation processes play the dominant role. No chemical interaction between the proangiogenic and antiangiogenic factors is assumed. The model is based on corneal pocket experiments, and provides a mathematical analysis of the initial spacing of angiogenic sprouts

Surface networks

© Copyright CASA, UCL. The desire to understand and exploit the structure of continuous surfaces is common to researchers in a range of disciplines. Few examples of the varied surfaces forming an integral part of modern subjects include terrain, population density, surface atmospheric pressure, physico-chemical surfaces, computer graphics, and metrological surfaces. The focus of the work here is a group of data structures called Surface Networks, which abstract 2-dimensional surfaces by storing only the most important (also called fundamental, critical or surface-specific) points and lines in the surfaces. Surface networks are intelligent and “natural ” data structures because they store a surface as a framework of “surface ” elements unlike the DEM or TIN data structures. This report presents an overview of the previous works and the ideas being developed by the authors of this report. The research on surface networks has fou

Tuning supersymmetric models at the LHC: A comparative analysis at two-loop level

We provide a comparative study of the fine tuning amount (Delta) at the two-loop leading log level in supersymmetric models commonly used in SUSY searches at the LHC. These are the constrained MSSM (CMSSM), non-universal Higgs masses models (NUHM1, NUHM2), non-universal gaugino masses model (NUGM) and GUT related gaugino masses models (NUGMd). Two definitions of the fine tuning are used, the first (Delta_{max}) measures maximal fine-tuning wrt individual parameters while the second (Delta_q) adds their contribution in "quadrature". As a direct result of two theoretical constraints (the EW minimum conditions), fine tuning (Delta_q) emerges as a suppressing factor (effective prior) of the averaged likelihood (under the priors), under the integral of the global probability of measuring the data (Bayesian evidence p(D)). For each model, there is little difference between Delta_q, Delta_{max} in the region allowed by the data, with similar behaviour as functions of the Higgs, gluino, stop mass or SUSY scale (m_{susy}=(m_{\tilde t_1} m_{\tilde t_2})^{1/2}) or dark matter and g-2 constraints. The analysis has the advantage that by replacing any of these mass scales or constraints by their latest bounds one easily infers for each model the value of Delta_q, Delta_{max} or vice versa. For all models, minimal fine tuning is achieved for M_{higgs} near 115 GeV with a Delta_q\approx Delta_{max}\approx 10 to 100 depending on the model, and in the CMSSM this is actually a global minimum. Due to a strong ($\approx$ exponential) dependence of Delta on M_{higgs}, for a Higgs mass near 125 GeV, the above values of Delta_q\approx Delta_{max} increase to between 500 and 1000. Possible corrections to these values are briefly discussed.Comment: 23 pages, 46 figures; references added; some clarifications (section 2

A 8-neighbor model lattice Boltzmann method applied to mathematical-physical equations

© 2016. This version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/A lattice Boltzmann method (LBM) 9-bit model is presented to solve mathematical-physical equations, such as, Laplace equation, Poisson equation, Wave equation and Burgers equation. The 9-bit model has been verified by several test cases. Numerical simulations, including 1D and 2D cases, of each problem are shown respectively. Comparisons are made between numerical predictions and analytic solutions or available numerical results from previous researchers. It turned out that the 9-bit model is computationally effective and accurate for all different mathematical-physical equations studied. The main benefits of the new model proposed is that it is faster than the previous existing models and has a better accuracy.Peer ReviewedPostprint (author's final draft

Moments and Lyapunov exponents for the parabolic Anderson model

We study the parabolic Anderson model in $(1+1)$ dimensions with nearest neighbor jumps and space-time white noise (discrete space/continuous time). We prove a contour integral formula for the second moment and compute the second moment Lyapunov exponent. For the model with only jumps to the right, we prove a contour integral formula for all moments and compute moment Lyapunov exponents of all orders.Comment: Published in at http://dx.doi.org/10.1214/13-AAP944 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org